1,755 research outputs found
A simple multigrid scheme for solving the Poisson equation with arbitrary domain boundaries
We present a new multigrid scheme for solving the Poisson equation with
Dirichlet boundary conditions on a Cartesian grid with irregular domain
boundaries. This scheme was developed in the context of the Adaptive Mesh
Refinement (AMR) schemes based on a graded-octree data structure. The Poisson
equation is solved on a level-by-level basis, using a "one-way interface"
scheme in which boundary conditions are interpolated from the previous coarser
level solution. Such a scheme is particularly well suited for self-gravitating
astrophysical flows requiring an adaptive time stepping strategy. By
constructing a multigrid hierarchy covering the active cells of each AMR level,
we have designed a memory-efficient algorithm that can benefit fully from the
multigrid acceleration. We present a simple method for capturing the boundary
conditions across the multigrid hierarchy, based on a second-order accurate
reconstruction of the boundaries of the multigrid levels. In case of very
complex boundaries, small scale features become smaller than the discretization
cell size of coarse multigrid levels and convergence problems arise. We propose
a simple solution to address these issues. Using our scheme, the convergence
rate usually depends on the grid size for complex grids, but good linear
convergence is maintained. The proposed method was successfully implemented on
distributed memory architectures in the RAMSES code, for which we present and
discuss convergence and accuracy properties as well as timing performances.Comment: 33 pages, 15 figures, accepted for publication in Journal of
Computational Physic
An adaptive Cartesian embedded boundary approach for fluid simulations of two- and three-dimensional low temperature plasma filaments in complex geometries
We review a scalable two- and three-dimensional computer code for
low-temperature plasma simulations in multi-material complex geometries. Our
approach is based on embedded boundary (EB) finite volume discretizations of
the minimal fluid-plasma model on adaptive Cartesian grids, extended to also
account for charging of insulating surfaces. We discuss the spatial and
temporal discretization methods, and show that the resulting overall method is
second order convergent, monotone, and conservative (for smooth solutions).
Weak scalability with parallel efficiencies over 70\% are demonstrated up to
8192 cores and more than one billion cells. We then demonstrate the use of
adaptive mesh refinement in multiple two- and three-dimensional simulation
examples at modest cores counts. The examples include two-dimensional
simulations of surface streamers along insulators with surface roughness; fully
three-dimensional simulations of filaments in experimentally realizable
pin-plane geometries, and three-dimensional simulations of positive plasma
discharges in multi-material complex geometries. The largest computational
example uses up to million mesh cells with billions of unknowns on
computing cores. Our use of computer-aided design (CAD) and constructive solid
geometry (CSG) combined with capabilities for parallel computing offers
possibilities for performing three-dimensional transient plasma-fluid
simulations, also in multi-material complex geometries at moderate pressures
and comparatively large scale.Comment: 40 pages, 21 figure
An efficient parallel immersed boundary algorithm using a pseudo-compressible fluid solver
We propose an efficient algorithm for the immersed boundary method on
distributed-memory architectures, with the computational complexity of a
completely explicit method and excellent parallel scaling. The algorithm
utilizes the pseudo-compressibility method recently proposed by Guermond and
Minev [Comptes Rendus Mathematique, 348:581-585, 2010] that uses a directional
splitting strategy to discretize the incompressible Navier-Stokes equations,
thereby reducing the linear systems to a series of one-dimensional tridiagonal
systems. We perform numerical simulations of several fluid-structure
interaction problems in two and three dimensions and study the accuracy and
convergence rates of the proposed algorithm. For these problems, we compare the
proposed algorithm against other second-order projection-based fluid solvers.
Lastly, the strong and weak scaling properties of the proposed algorithm are
investigated
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